Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition

2008/01/31 by Shu Chen, Li Wang, Yajiang Hao +1 · 14 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.other #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreva.77.032111

published as Phys. Rev. A 77, 032111 (2008) · 5 pages, 3 figures

openalex publication_date 2008/03/24 · arxiv created 2008/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notion of fidelity in quantum information science has been recently applied to analyze quantum phase transitions from the viewpoint of the ground-state (GS) overlap for various many-body systems. In this work, we unveil the intrinsic relation between the GS fidelity and the derivatives of GS energy and find that they play an equivalent role in identifying the quantum phase transition. The general connection between the two approaches enables us to understand the different singularity and scaling behaviors of fidelity exhibited in various systems on general grounds. Our general conclusions are illustrated via several quantum spin models which exhibit different kinds of quantum phase transitions.

Citations

• Two soluble models of an antiferromagnetic chain

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• Entanglement modes and topological phase transitions in superconductors
• Reduced fidelity in the Kitaev honeycomb model
• Quantum phase transition in easy-axis antiferromagnetic Heisenberg spin-1 chain
• Characterization of topological phase transitions via topological properties of transition points
• Reduced fidelity and quantum phase transitions in spin-1/2 frustrated Heisenberg chains
• Reduced fidelity susceptibility and its finite-size scaling behaviors in the Lipkin-Meshkov-Glick model
• Linking phase transitions and quantum entanglement at arbitrary temperature

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